Dynamical Systems Seminar: Lev A. Ostrovsky
Self-synchronization in an ensemble of nonlinear oscillators
Lev A. Ostrovsky
听(狈翱础础)听, 麻豆影院, CO
Date and time:听
Thursday, December 4, 2014 - 2:00pm
尝辞肠补迟颈辞苍:听
ECCR 257
础产蝉迟谤补肠迟:听
Collective behavior of nonlinear oscillators is of interest from different viewpoints including physical and biological applications, as well as in the dynamical theory of multi-dimensional systems. This behavior has been studied for different systems using different approaches. An important set of studies, started by Kuramoto, is referred to a set of phase-coupled oscillators having a fixed amplitude. Here we describe another group of works related to systems of coupled nonlinear oscillators which can change both amplitudes and phases in the course of interaction. Such systems can model various physical phenomena and devices such as classical versions of super-radiance of electrons, electromagnetic generators based on cooperative radiation of electrons (鈥済yrotron鈥), as well as to the problem of 鈥淪aser,鈥 an acoustic analog of laser. The main features of the self-synchronization process are considered for a system of Duffing-type oscillators with two types of coupling, dissipative and reactive; in the latter case the system is conservative (Hamiltonian). First, the analytical approach is outlined which allows to find the condition of instability in an initially incoherent system, and to approximately describe the nonlinear regime of the coherent field generation using a 鈥渕odal鈥 approach. Then the direct numerical calculation of systems of 100 to 1000 equations is performed and processed. Whenever possible, these results are compared with analytical ones.听 Some relevant physical systems and the issues to be solved are mentioned.
The recent part of the presented results was obtained in collaboration with E. A. Skirta and E. V. Galperin (East Stroudsburg University, East Stroudsburg, PA).